Even though the Nova-class was designed to travel at a maximum speed of warp factor 8, when the USS Equinox powered its warp drive with energy derived from the corpses of nucleogenic lifeforms, an increase of 0.03% was added to the warp factor, allowing the velocity of traveling ten thousand light years in less than two weeks. (VOY: "Equinox")

As noted above, the tolerance of a ship's systems for the stresses of warp travel are a primary limiting factor, so while exceeding the ship's maximum rated speed can be technically possible, it carries the risk of severe damage to the warp drive or to the ship's structural integrity.

When a ship is ordered to accelerate to maximum warp, it does not always mean the absolute highest reachable warp factor. For example, in ENT: "Affliction", the Enterprise NX-01 already travels at maximum warp, but then accelerates to warp 5.2. In both TNG: "Time Squared" and TNG: "Bloodlines", maximum warp denoted warp 9, although the Enterprise-D was established to be capable of faster speeds in other episodes. A similar situation occurred in DS9: "The Sound of Her Voice", when the USS Defiant, traveling at maximum warp, accelerates to warp 9.5.